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A256037 Triangle read by rows: number of R-class idempotents of rank k in Brauer monoid B_n. 0

%I

%S 1,0,1,1,0,1,0,3,0,1,3,0,5,0,1,0,15,0,7,0,1,15,0,35,0,9,0,1,0,105,0,

%T 63,0,11,0,1,105,0,315,0,99,0,13,0,1,0,945,0,693,0,143,0,15,0,1,945,0,

%U 3465,0,1287,0,195,0,17,0,1

%N Triangle read by rows: number of R-class idempotents of rank k in Brauer monoid B_n.

%H I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., <a href="http://arxiv.org/abs/1408.2021">Enumeration of idempotents in diagram semigroups and algebras</a>, arXiv preprint arXiv:1408.2021 [math.GR], 2014.

%F Conjecture: T(n,k) = (n+k-1)!!/(2k-1)!! for n+k even, T(n,k) = 0 otherwise. - _Jean-Fran├žois Alcover_, Feb 11 2019

%e Triangle begins:

%e 1,

%e 0, 1,

%e 1, 0, 1,

%e 0, 3, 0, 1,

%e 3, 0, 5, 0, 1,

%e 0, 15, 0, 7, 0, 1,

%e 15, 0, 35, 0, 9, 0, 1,

%e 0, 105, 0, 63, 0, 11, 0, 1,

%e 105, 0, 315, 0, 99, 0, 13, 0, 1,

%e 0, 945, 0, 693, 0, 143, 0, 15, 0, 1,

%e 945, 0, 3465, 0, 1287, 0, 195, 0, 17, 0, 1,

%e ...

%K nonn,tabl

%O 0,8

%A _N. J. A. Sloane_, Mar 14 2015

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Last modified March 25 15:02 EDT 2019. Contains 321470 sequences. (Running on oeis4.)